Nonsmooth Calabi-Yau structures for algebras and coalgebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913746891309056 |
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| author | Booth, Matt Chuang, Joseph Lazarev, Andrey |
| author_facet | Booth, Matt Chuang, Joseph Lazarev, Andrey |
| contents | We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul dual properties. As an application, we give a new characterisation of Poincaré duality spaces, which extends a theorem of Félix- Halperin-Thomas to the non-simply connected setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonsmooth Calabi-Yau structures for algebras and coalgebras Booth, Matt Chuang, Joseph Lazarev, Andrey Rings and Algebras Algebraic Geometry Algebraic Topology K-Theory and Homology Representation Theory 18N40, 16E65, 14A22, 57P10 We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul dual properties. As an application, we give a new characterisation of Poincaré duality spaces, which extends a theorem of Félix- Halperin-Thomas to the non-simply connected setting. |
| title | Nonsmooth Calabi-Yau structures for algebras and coalgebras |
| topic | Rings and Algebras Algebraic Geometry Algebraic Topology K-Theory and Homology Representation Theory 18N40, 16E65, 14A22, 57P10 |
| url | https://arxiv.org/abs/2502.12162 |